A correction to, and a more complete proof of, Theorem 1 of Fuhrmann and Miller (see ibid., vol.34, no.7, p.722-29, 1988) is given. We consider the existence of solutions to the maximum-likelihood (ML) structured covariance estimation problem. In particular, we are interested in determining the circumstances under which the log likelihood is unbounded above for a given covariance constraint set R ...
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Let ρ(1,m) and N(1,m) be the covering radius and norm of the first-order Reed-Muller code R(1,m), respectively. It is known that ρ(1,2k+1)&les;lower bound [22k-2(2k-1/2)] and N(1,2k+1)&les;2 lower bound [22k-2(2k-1/2)] (k>0). We prove that ρ(1,2k+1)&les;2 lower bound [22k-1-2(2k-3/2)] and N(1,2k+1)&les;4 lower bound [...
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This paper considers the achievable accuracy in jointly estimating the parameters of a real-valued two-dimensional (2-D) homogeneous random field with mixed spectral distribution, from a single observed realization of it. On the basis of a 2-D Wold-like decomposition, the field is represented as a sum of mutually orthogonal components of three types: purely indeterministic, harmonic, and evanescen...
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Some binary linear codes of length 50 and 100 are constructed using the adjacency matrices of the Hoffman-Singleton graph and the Higman-Sims graph, Some of the codes are optimal or nearly optimal for the given length and dimension. The dual codes admit majority logic decoding
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We give degree of approximation results for decision regions which are defined by polynomial and neural network parametrizations. The volume of the misclassified region is used to measure the approximation error, and results for the degree of L1 approximation of functions are used. For polynomial parametrizations, we show that the degree of approximation is at least 1, whereas for neura...
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We present a decoding procedure for Reed-Solomon (RS) and BCH codes defined over an integer residue ring pgZq, where q is a power of a prime p. The proposed decoding procedure, as for RS and BCH codes over fields, consists of four major steps: (1) calculation of the syndromes; (2) calculation of the “elementary symmetric functions,” by a modified Berlekamp-Massey (1...
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New upper and lower bounds on the mean recovery time of decision feedback equalization (DFE) are derived. The recovery time is defined as the time it takes the decision feedback equalizer (DFEQ) to reach the error-free state after an error has corrupted an error-free DFEQ. The derivations of the bounds assume a causal channel response, independent data symbols, and independent noise samples. The b...
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A communication network with tine-varying topology is considered. The network consists of M receivers and N transmitters that, in principle, may access every receiver. An underlying network state process with Markovian statistics is considered that reflects the physical characteristics of the network affecting the link service capacity. The transmissions are scheduled dynamically, based on informa...
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Let the kth-order empirical distribution of a code be defined as the proportion of k-strings anywhere in the codebook equal to every given k-string. We show that for any fixed k, the kth-order empirical distribution of any good code (i.e., a code approaching capacity with vanishing probability of error) converges in the sense of divergence to the set of input distributions that maximize the input/...
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A new class of pseudo-random sequences (called cascaded GMW-type permutation polynomial (CGPP) sequences) over GP(qn) is constructed using a system of n orthogonal cascaded GMW functions in GF(q). Their statistical properties are given. Classification, evaluation, and implementation of the CGPP sequences are derived. A sequence generated by mapping elements of a CGPP sequence into GF(q)...
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A unified framework is presented in order to build lattice constellations matched to both the Rayleigh fading channel and the Gaussian channel. The method encompasses the situations where the interleaving is done on the real components or on two-dimensional signals. In the latter case, a simple construction of lattices congruent to the densest binary lattices with respect to the Euclidean distance...
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The largest quasi-cyclic subcode of the Reed-Muller code R(r,m), invariant under the shift T2m-l is determined. This code, denoted QCR(r,m,l), is presented through its module decomposition into cyclic submodules. The smallest regular trellis diagram (SRTD) is defined for block codes. This trellis and its construction algorithm are given for the class of cyclic-form codes. Using the cycl...
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The paper is devoted to spatial adaptive estimation of signals satisfying linear differential inequalities with an unknown differential operator of a given order. The classes of signals under consideration cover a wide variety of classes common to nonparametric regression. In particular, they contain the signals whose parameters of smoothness are not uniformly bounded, even locally. We develop an ...
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This paper describes how 2-adic numbers can be used to analyze the structure of binary cyclic codes and of cyclic codes defined over Z 2(a), a&ges;2, the ring of integers modulo 2a. It provides a 2-adic proof of a theorem of McEliece that characterizes the possible Hamming weights that can appear in a binary cyclic code. A generalization of this theorem is derived th...
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This correspondence presents a new coding scheme based on a combinatory detecting set for synchronous code-division multiple-access (S-CDMA) systems, which can support a number of users far exceeding current S-CDMA approaches. Examples of code construction and decoding are also given
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A detailed analysis of the maximum aperiodic autocorrelation of the original Chu sequences (equivalently, P3/P4 pulse compression codes) is presented. The result implies the best known upper bound on the minimax aperiodic autocorrelation for polyphase sequences except when the length is very small or a perfect square. It is well known that determining the minimax aperiodic correlation for polyphas...
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In this correspondence, the exact weight distribution for closest coset decoding of |u|u+v| constructed codes is derived. The results allow more accurate evaluations of the decoding error probabilities
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We consider a slotted ring that allows simultaneous transmissions of messages by different nodes, known as ring with spatial reuse. To alleviate fairness problems that arise in such networks, policies have been proposed that operate in cycles and guarantee that a certain number of packets, not exceeding a given number called a quota, will be transmitted by every node in every cycle. We provide suf...
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The study of matrices with a displacement structure is mainly concerned with recursions for the so-called generator matrices. The recursion usually involves free parameters, which can be chosen in several ways so as to simplify the resulting algorithm. In this correspondence we present a choice for the parameters that is motivated by a maximum-entropy formulation, This choice further motivates the...
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The (noiseless) fixed-length source coding theorem states that, except for outcomes in a set of vanishing probability, a source can be encoded at its entropy but not more efficiently. It is well known that the asymptotic equipartition property (AEP) is a sufficient condition for a source to be encodable at its entropy. This paper shows that the AEP is necessary for the source coding theorem to hol...
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We determine the dimensions of subfield codes of Reed-Solomon codes and construct certain extensions and lengthenings of these codes. We start from the duals, using the language of orthogonal arrays. As a first result this allows us to obtain a fair number of improvements in the list of binary, ternary, and quaternary linear codes with largest known minimal distance
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Cosets of convolutional codes can be used to obtain large free Euclidean distances and short maximum zero-run lengths at the output of the 1-D partial-response channel (PRC). We present a new soft-decision decoding technique for cosets of convolutional codes on the preceded 1-D PRC. The decoding technique is especially well suited for cosets of partial unit memory (PUM) convolutional codes. A conn...
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We derive new estimates for the range of binomiality in a code's spectra, where the distance distribution of a code is upperbounded by the corresponding normalized binomial distribution. The estimates depend on the code's dual distance
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